Date/Time : 29 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Janosch Ortmann, University of Quebec in Montreal

The probabilistic coupling approach to study stochastic planar models originated in the works of Cator and Groeneboom on Hammersley’s process and the Poisson last-passage percolation (LPP). It has since been developed to treat many aspects of the KPZ universality in various models of directed LPP, directed polymers and interacting particles.

In this talk I will discuss two variants of the exponential LPP model: the bulk model, where the last-passage environment is given by independent Exp(1)-distributed weights on the integer quadrant and the (two-sided) boundary model, where an additional layer of independent Exp(w)-distributed weights are placed on the horizontal boundary and independent Exp(1-z)-distributed weights on the vertical boundary, for $0<w,z<1$. A particular interest for the increment-stationary case ($w=z$) arises from the fact that then the distribution of the LPP increments is invariant under lattice shifts.

I will discuss how the coupling framework can be used to derive optimal-order upper and lower bounds on the central moment for these two variants of exponential LPP. That is, letting $v$ be the LPP end-point we obtain bounds proportional to $\|v\|^{p/2}$ (CLT scaling) when $v$ is close to the axis and to $\|v\|^{p/3}$ (KPZ regime) otherwise. These bounds are also uniform over vertices taking values in these regions.

The talk is based on joint work with Elnur Emrah and Nicos Georgiou.

Add to calendar :

Date/Time : 23 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Roberto Imbuzeiro Oliveira , Instituto Nacional de Matemática Pura e Aplicada (IMPA)

Estimating the mean of a random vector from i.i.d. data has received considerable attention. When the data take values in more general metric spaces, an appropriate extension of the notion of the mean is the Fréchet mean. While asymptotic properties of the most natural Fréchet mean estimator (the empirical Fréchet mean) have been
thoroughly researched, non-asymptotic performance bounds have only been studied recently.

This talk considers the performance of estimators of the Fréchet mean in general metric spaces under possibly heavy-tailed and contaminated data. In such cases, the empirical Fréchet mean is a poor estimator. We propose a general estimator based on high-dimensional extensions of trimmed means and prove general performance bounds. Unlike all previously established bounds, ours generalize the optimal bounds known for Euclidean data. Much like in the Euclidean case, the optimal accuracy is governed by two “variance” terms: a “global variance” term that is independent of the prescribed confidence, and a potentially much smaller, confidence-dependent “local variance” term. We apply our results for metric spaces with curvature bounded from below, such as Wasserstein spaces, and for uniformly convex Banach spaces.

The talk is based on arXiv:2509.13606, which is joint work with Daniel Bartl (NUS), Gabor Lugosi (ICREA/UPF), and Zoraida Rico (Bocconi).

Add to calendar :

Date/Time : 15 Oct 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Vladimir Spokoiny, Weierstrass Institute for Applied Analysis and Stochastics (WIAS)

The recent paper Gao et al. (2023) on estimation and inference for top-ranking problem in Bradley-Terry-Luce (BTL) model presented a surprising result: component-wise estimation and inference can be done under much weaker conditions on the number of comparison then it is required for the full dimensional estimation. The present paper revisits this finding from completely different viewpoint. Namely, we show how a theoretical study of estimation in sup-norm can be reduced to the analysis of plug-in semiparametric estimation. For the latter, we adopt and extend the general approach from Spokoiny (2025b) to high-dimensional estimation and inference. The main tool of the analysis is a theory of perturbed marginal optimization when an objective function depends on a low-dimensional target parameter along with a high-dimensional nuisance parameter. A particular focus of the study is the critical dimension condition. Full-dimensional estimation requires in general the condition n ≫ p between the effective parameter dimension p and the effective sample size corresponding to the smallest eigenvalue of the Fisher information matrix . Inference on the estimated parameter is even more demanding: the condition n ≫ p^2 cannot be generally avoided; see Spokoiny (2025b). However, for the sup-norm estimation, the critical dimension condition can be reduced to n ≥ C log p.

Add to calendar :

Date/Time : 01 Oct 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Akshay Hegde , National University of Singapore

Analysing the critical point structure of smooth Gaussian fields on $\mathbb{R}^d$ has been paramount in various probability problems. For example, the excursion probability P( sup f >u) can be precisely estimated by counting the number of critical points above the level u. Other examples include optimization of spherical spin glass models, percolation of level sets of smooth Gaussian fields. In this talk, we’ll explore the Poisson structure of high critical points of stationary smooth Gaussian fields. This is joint work with Dmitry Belyaev. 

Add to calendar :

Date/Time : 19 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

Add to calendar :

Date/Time : 18 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

Add to calendar :

Date/Time : 12 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

Add to calendar :

Date/Time : 11 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

Add to calendar :

Date/Time : 10 Sep 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Fanhao Kong, Peking University

We consider a class of weakly asymmetric continuous microscopic growth models with polynomial smoothing mechanisms, general nonlinearities and a Poisson type noise. We show that they converge to the KPZ equation after proper rescaling, where the coupling constant depends on all details of the smoothing and growth mechanisms in the microscopic model. This provides a first example of Hairer-Quastel type with both generic nonlinearity and non-Gaussian noise. This talk is based on the joint work with Haiyi Wang and Weijun Xu.

Add to calendar :